The battle for the GOP presidential nomination is also tied at the top. Former Massachusetts Gov. Mitt Romney has the backing of 31 percent of likely Republican caucus-goers, while 28 percent support former Arkansas Gov. Mike Huckabee. Taking into account the survey’s sampling error of 5 percentage points in the GOP race, it’s a statistical dead heat between Romney and Huckabee.

Former Sen. Fred Thompson of Tennessee places third in the poll at 13 percent with Sen. John McCain of Arizona 3 points back. Former New York City Mayor Rudy Giuliani is at 8 percent, as is Rep. Ron Paul of Texas.

Rep. Duncan Hunter of California is at less than 0.5 of 1 percent.

Romney gained 6 points since the last CNN poll in Iowa, taken in mid December, with Huckabee dropping 5 points in the same time. Huckabee has lost ground “mostly among higher income Republicans and GOP’s under 50 years old,” said Holland.

“Romney support has risen entirely among women, where it doubled over the last two weeks,” said Schneider.